1. Field of the Invention
The present invention relates to a logarithmic amplifier which generates an output voltage proportional to a logarithmic value of input current value and, for example, is used in radiation measuring circuits.
2. Description of the Prior Art
FIG. 1 is a circuit indicating an example of the conventional logarithmic amplifier. In this figure, 1 is an input terminal, 2 is an operatin amplifier, and 3 is a transistor used as a logarithmic conversion feedback element of operational amplifier 2. The collector of transistor 3 is connected to an inversion input terminal of operational amplifer 2 and the emitter is connected to an output terminal 4 of the operational amplifier 2. 31, 32 are respectively internal resistances provided between the emitter-base junction of transistor 3 and external electrodes.
Operations are explained hereunder.
The relationship between collector current I.sub.c and base-emitter voltage V of the transistor 3 is expressed by the following equation. EQU I.sub.c =I.sub.s (e.sup.qv/kT -1) (1)
Here,
I.sub.s : backward saturation current PA1 q: electron charge PA1 k: Boltzman's constant PA1 T: absolute temperature
The equation (1) can be transformed as follows. ##EQU1##
Here, since I.sub.s is much smaller than I.sub.c, it can be omitted and thereby the equation (2) can be simplified as follows. ##EQU2##
When an input current is applied to the input terminal 1 in the circuit of FIG. 1, the input current becomes a collector current I.sub.c of transistor 3 by the effect of operational amplifier 2 and a logarithmic voltage V indicated by the equation (3) is generated at the emitter of transistor 3. This voltage can be detected from the output terminal 4.
Therefore, a voltage proportional to a logarithmic input current value can be obtained at the output terminal 4 by supplying an input current to the input terminal 1 of the circuit of FIG. 1.
Since the conventional logarithmic amplifier is constituted as explained above, a logarithmic voltage including a voltage drop across internal resistances 31, 32 of the emitter electrode and base electrode of the transistor 3 is obtained. Namely, the equation (1) is applied to the ideal transistor and a voltage V of the equation (3) of actual transistor 3 is not an accurate logarithmic voltage value. When the internal resistances 31, 32 are R.sub.31, R.sub.32, emitter current is I.sub.e, and base current is I.sub.b, a logarithmic voltage value V.sub.r including the effect of internal resistances can be expressed by the following equation. ##EQU3##
The second term of equation (4) is an error for logarithmic characteristic. A larger input current results in a larger error, raising a problem that the maximum value of input current is limited.